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Submodular set function

Known as: Submodular, Submodular function 
In mathematics, a submodular set function (also known as a submodular function) is a set function whose value, informally, has the property that the… Expand
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Active learning (machine learning)Alexander SchrijverArtificial intelligenceAutomatic summarization
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Broader (1)

Combinatorial optimization

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2011
Highly Cited
2011
Maximizing Non-monotone Submodular Functions
Submodular maximization generalizes many important problems including Max Cut in directed and undirected graphs and hypergraphs… Expand
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Highly Cited
2007
Highly Cited
2007
Maximizing a Submodular Set Function Subject to a Matroid Constraint (Extended Abstract)
Let $f:2^{N} \rightarrow \cal R^{+}$ be a non-decreasing submodular set function, and let $(N,\cal I)$ be a matroid. We consider… Expand
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Highly Cited
2004
Highly Cited
2004
A note on maximizing a submodular set function subject to a knapsack constraint
In this paper, we obtain an (1-e^-^1)-approximation algorithm for maximizing a nondecreasing submodular set function subject to a… Expand
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Highly Cited
2001
Highly Cited
2001
A combinatorial strongly polynomial algorithm for minimizing submodular functions
This paper presents a combinatorial polynomial-time algorithm for minimizing submodular functions, answering an open question… Expand
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Highly Cited
2000
Highly Cited
2000
A Combinatorial Algorithm Minimizing Submodular Functions in Strongly Polynomial Time
We give a strongly polynomial-time algorithm minimizing a submodular function f given by a value-giving oracle. The algorithm… Expand
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Highly Cited
1982
Highly Cited
1982
An analysis of the greedy algorithm for the submodular set covering problem
AbstractWe consider the problem: min $$\{ \mathop \Sigma \limits_{j \in s} f_j :z(S) = z(N),S \subseteqq N\} $$ wherez is a… Expand
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Highly Cited
1978
Highly Cited
1978
An analysis of approximations for maximizing submodular set functions—I
LetN be a finite set andz be a real-valued function defined on the set of subsets ofN that satisfies z(S)+z(T)≥z(S⋃T)+z(S⋂T) for… Expand
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Highly Cited
1978
Highly Cited
1978
Minimizing a Submodular Function on a Lattice
This paper gives general conditions under which a collection of optimization problems, with the objective function and the… Expand
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Highly Cited
1978
Highly Cited
1978
Best Algorithms for Approximating the Maximum of a Submodular Set Function
A real-valued function z whose domain is all of the subsets of N = {1,..., n is said to be submodular if zS + zT ≥ zS ∪ T + zS… Expand
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Highly Cited
1978
Highly Cited
1978
Accelerated greedy algorithms for maximizing submodular set functions
Given a finite set E and a real valued function f on P(E) (the power set of E) the optimal subset problem (P) is to find S ⊂ E… Expand
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